Hierarchically structural and biphillic surface energy designs for enhanced condensation heat transfer

ABSTRACT

An apparatus comprising a base layer, a distribution of separated micro-nucleation sites thereon. The apparatus also includes a distribution nanostructures located on the base layer, each of the micro-nucleation sites being adjacent to some of the nanostructures. Each of the micro-nucleation sites has a hydrophilic surface and the distribution of nanostructures form a superhydrophobic surface.

TECHNICAL FIELD

The invention relates to in general, heat transfer devices, and methodsfor manufacturing the same.

BACKGROUND

This section introduces aspects that may help facilitate a betterunderstanding of the inventions. Accordingly, the statements of thissection are to be read in this light and are not to be understood asadmissions about what is prior art or what is not prior art.

Condensation is an important process in a number of two-phase heattransfer apparatuses implemented for thermal management. Improving theefficiency of such condensation heat transfer processes has thepotential to enable size reductions of heat transfer apparatuses whilestill achieving the same overall heat transfer performance.

SUMMARY

One embodiment is an apparatus comprising a base layer having adistribution of separated micro-nucleation sites thereon. The apparatusalso includes a distribution of nanostructures located on the baselayer, each of the micro-nucleation sites being adjacent to some of thenanostructures; and wherein each of the micro-nucleation sites has ahydrophilic surface and the distribution of nanostructures form asuperhydrophobic surface.

In any of the above embodiments of the apparatus, the micro-nucleationsites and the nanostructures are located on a planar surface of the baselayer. In some embodiments tops of the nanostructures are substantiallycoplanar with the hydrophilic surfaces of the micro-nucleation sites. Insome embodiments, some of the nanostructures surround each of themicro-nucleation sites. In some embodiments, the hydrophilic surfaces ofeach of the micro-nucleation sites are substantially coplanar withbottoms of the nanostructures that contact the base layer. In someembodiments, the hydrophilic surface of each of the micro-nucleationsites has a smooth surface. In some embodiments, an area occupied by thehydrophilic surfaces of each of the micro-nucleation sites is in a rangeof 1 to 100 microns². In some embodiments, a separation distance betweenadjacent ones of the micro-nucleation sites is equal to or less thanabout 10 microns. In some embodiments, the nanostructures are located ona region of the base layer having a lower thermal conductivity than aregion of the base layer having the micro-nucleation sites thereon. Insome embodiments, wherein tops of the nanostructures include a reentrantangled ledge. In some embodiments, an area of the base layer having thenanostructures located thereon has a surface roughness where thefollowing condition applies when a liquid droplet rests on the surface:−1/r*cos θa<1, wherein r is the surface roughness of the surfaces havingthe distribution of nanostructures located thereon and ea is anintrinsic advancing contact angle of the liquid droplet. In someembodiments, a distance between adjacent ones of the nanostructures isgreater than a critical condensation radius for a nucleating liquiddroplet on the surface.

One embodiment is a system. The system comprises heat generatingequipment and a heat transfer apparatus configured to remove heatgenerated by the electronic equipment. The apparatus includes a baselayer having a distribution of separated micro-nucleation sites thereon.The apparatus includes a distribution of nanostructures located on thebase layer, each of the micro-nucleation sites being adjacent to some ofthe nanostructures. Each of the micro-nucleation sites has a hydrophilicsurface and the distribution of nanostructures form a superhydrophobicsurface.

In some embodiments of the system, the micro-nucleation sites arelocated on the surface of a condenser of the apparatus. In someembodiments, the condenser is part of a heat pipe or a vapor chamber.

Another embodiment is a method. The method comprises manufacturing acondenser, including: providing a base layer and forming a distributionof separated micro-nucleation sites on the base layer, wherein each ofthe micro-nucleation sites has a hydrophilic surface. Manufacturing thecondenser also includes forming a distribution nanostructures on thebase layer, wherein each of the micro-nucleation sites being adjacent tosome of the nanostructures.

In any of the above embodiments of the method, forming themicro-nucleation sites includes forming a mask layer over the base layerand patterning the mask layer such that mask portions remain on the baselayer in locations corresponding to the micro-nucleation sites. In someembodiments, forming the nanostructures on the base layer includesmodifying portions of the base layer not covered by mask portionslocated on the base layer that correspond to locations of themicro-nucleation sites. In some such embodiments, forming themicro-nucleation sites includes removing the mask portions to uncoverthe micro-nucleation sites such that tops of the nanostructures aresubstantially coplanar with the hydrophillic surfaces of themicro-nucleation sites. In some embodiments, forming the nanostructureson the base layer includes forming a mask layer over the base layer,patterning the mask layer such that mask portions remain on the baselayer corresponding to locations of the micro-nucleation sites, forminga material layer on the base layer and the mask portions and modifyingthe material layer on the base layer and the mask portions to form thenanostructures.

BRIEF DESCRIPTION OF THE DRAWINGS

The embodiments of the disclosure are best understood from the followingdetailed description, when read with the accompanying FIGUREs. Somefeatures in the figures may be described as, for example, “top,”“bottom,” “vertical” or “lateral” for convenience in referring to thosefeatures. Such descriptions do not limit the orientation of suchfeatures with respect to the natural horizon or gravity. Variousfeatures may not be drawn to scale and may be arbitrarily increased orreduced in size for clarity of discussion. Reference is now made to thefollowing descriptions taken in conjunction with the accompanyingdrawings, in which:

FIG. 1 presents a cross-sectional view of an apparatus;

FIG. 2 presents a plan view of the apparatus shown in FIG. 1 along viewline 2-2 in FIG. 1;

FIG. 3A presents a cross-sectional view of an alternative apparatus,analogous to the view presented in FIG. 1;

FIG. 3B presents a cross-sectional view of an another alternativeapparatus, analogous to the view presented in FIG. 1;

FIG. 4 presents a detailed cross-sectional view of one embodiment ofnanostructures;

FIG. 5 presents a flow diagram of an example method of manufacturing aheat transfer apparatus, such as any of the apparatuses described in thecontext of FIGS. 1-4;

FIG. 6A presents a cross-sectional view of the apparatus shown in FIG. 1at an intermediate stage of fabrication;

FIG. 6B presents a cross-sectional view of the apparatus shown in FIG. 1at another intermediate stage of fabrication;

FIG. 6C presents a cross-sectional view of the apparatus shown in FIG. 1at another intermediate stage of fabrication;

FIG. 7A presents a cross-sectional view of the apparatus shown in FIG.3A an intermediate stage of fabrication;

FIG. 7B presents a cross-sectional view of the apparatus shown in FIG.3A at another intermediate stage of fabrication;

FIG. 7C presents a cross-sectional view of the apparatus shown in FIG.3A at another intermediate stage of fabrication;

FIG. 7D presents a cross-sectional view of the apparatus shown in FIG.3A at another intermediate stage of fabrication;

FIG. 8 presents a block diagram of a system.

In the Figures and text, similar or like reference symbols indicateelements with similar or the same functions and/or structures.

In the Figures, the relative dimensions of some features may beexaggerated to more clearly illustrate one or more of the structures orfeatures therein.

Herein, various embodiments are described more fully by the Figures andthe Detailed Description. Nevertheless, the inventions may be embodiedin various forms and are not limited to the embodiments described in theFigures and Detailed Description of Illustrative Embodiments.

DETAILED DESCRIPTION

The description and drawings merely illustrate the principles of theinventions. It will thus be appreciated that a person of ordinary skillin the relevant arts will be able to devise various arrangements that,although not explicitly described or shown herein, embody the principlesof the inventions and are included within its scope. Furthermore, allexamples recited herein are principally intended expressly to be forpedagogical purposes to aid the reader in understanding the principlesof the inventions and concepts contributed by the inventor(s) tofurthering the art, and are to be construed as being without limitationto such specifically recited examples and conditions. Moreover, allstatements herein reciting principles, aspects, and embodiments of theinventions, as well as specific examples thereof, are intended toencompass equivalents thereof. Additionally, the term, “or,” as usedherein, refers to a non-exclusive or, unless otherwise indicated. Also,the various embodiments described herein are not necessarily mutuallyexclusive, as some embodiments can be combined with one or more otherembodiments to form new embodiments.

The use of non-wetting surfaces can enhance heat transfer coefficients,in comparison to smooth surfaces. Surprisingly, when the non-wettingsurface is a provided in the form of a surface covered withnanostructures, similar enhanced heat transfer coefficients have notbeen fully realized. In the earlier stages of a droplet's growthin-between and on the surfaces of nanostructures, growth is impeded bythe droplet's adhesion (or pinning) to the nanostructures. Additionally,thermal resistance at the early stage of droplet growth is associatedwith the large curvature of small droplets. This leads to a lowering ofthe local saturation pressure of the water vapor, reducing the drivingpotential for water vapor condensing into liquid water. Impeded growthof the droplet presents sources of thermal resistance which decreasesthe efficiency of heat transfer.

It is believed that these sources of thermal resistance can be mitigatedby providing a heat transfer apparatus with condensation surfaces havingseparate hierarchical structures thereon, i.e., separate structures withtwo different length scales, and, having biphilic surface energies,i.e., two different surface energies. The two different length scales ofthe hierarchically structures are micron-scaled structural features(“microstructures”) and nanometer-scaled structural features(“nanostructures”).

One embodiment is an apparatus (e.g., a heat transfer device). FIG. 1presents a cross-sectional view of an embodiment of the apparatus 100.FIG. 2 presents a plan view, at a lower magnification scale, of theapparatus 100 shown in FIG. 1 along view line 2-2 in FIG. 1.

As illustrated in FIG. 1, in some cases the apparatus 100 includes or isa condenser 105. The condenser 105 can be part of a variety of differenttwo-phase heat transfer apparatuses such as, but not limited to, heatpipes, vapor chambers, looped heat pipes or two-phase forced convectionflow loops. For example, in some cases, the condenser 105 can be aportion of the heat transfer apparatus 100 configured as a heat pipewhich further includes an evaporator portion 107. In still otherembodiments the condenser can be used in heat transfer apparatuses suchas compact condensers for electronics thermal management, e.g., inelectronics thermal management, e.g., in telecommunications and datacenters, industrial condensation heat exchangers, evaporator coils,dehumidifying coils, or water harvesting devices.

The apparatus 100, and in some cases the condenser 105, includes a baselayer 110 having one or more micro-nucleation sites 115 thereon, whereineach of the micro-nucleation sites 115 has a smooth surface 117. Theapparatus 100 also includes nanostructures 120 located on the base layer110 and around the micro-nucleation site 115. Tops 125 of thenanostructures 120 (e.g., a group 122 of tops 125) has a lower surfaceenergy than a surface energy of the smooth surface 120.

It is believed that the growth of droplets is promoted by providing themicro-nucleation sites 115 with a smooth, high energy surface 120.Droplet growth on such micro-nucleation sites 115 is promoted becausethe energy barriers associated with vapor condensing to a liquid stateare low such that the nucleation rate is large. This is in contrast tothe surrounding nanostructures that have a low intrinsic surface energy.Droplet growth from the high-surface-energy sites also significantlyreduces the curvature resistance as compared to droplets growing amongnanostructures or low-surface-energy regions in general.

As droplet grows on a micro-nucleation site 115 it will reach a largeenough size to contact the nanostructures 120 around the site 115.Because the nanostructure tops 125 (e.g., groups 122 of tops 125)surrounding the micro-nucleation sites 115 has a relatively lowersurface energy than the smooth surface 117 of the site 115, the growingdroplet is prompted to reach a Cassie state on the tops 125. The lowadhesion energy of the droplet on the tops 125 of the nanostructures 120in turn facilitates the droplet to spontaneously leave, or jump off,e.g., when they coalesce with droplets formed on neighboringmicro-nucleation sites. Furthermore, the spacing between themicro-nucleation sites is preferably above a minimum threshold topromote such droplet jumping. The spacing is determined by therelationship between the size of the micro-nucleation site 115 r and thespacing between the micro-nucleation sites 105.

As used herein, the term micro-nucleation site 115, refers to astructure that has at least linear one-dimension 127 adjacent to thebase layer 110 (e.g., a base width or depth) that extends a distanceacross the micro-nucleation site 115 in a range of 1 to 1000 microns.

As used herein, the term nanostructure 120, refers to a structure thathas at least one linear dimension (e.g. height, width, or depth) thatextends a distance from one side to an opposing side (e.g., opposinglateral sides 130, 132, or, top 125 and bottom side 135) of thenanostructure 120 in a range from 1 to 1000 nanometers. Additionally,the one linear dimension of the nanostructure 120 is at least 10 timessmaller than the one dimension 127 of the microstructure 115. As anon-limiting example, when the one dimension 127 of the microstructure115 equals 1 micron, then the one dimension of the nanostructure 120 canbe up to 100 nanometers. Consequently, in this example, the at least onelinear dimension of the nanostructure 120 (e.g., height, width, ordepth), can be in a range of 1 to 100 nanometers. As anothernon-limiting example, when the one dimension 127 of the microstructure115 equals 100 microns, then the one dimension of the nanostructure 120can be up to 1000 nanometers. Consequently, in this example, the onedimension of the nanostructure 120 (e.g., height, width, or depth), canbe in a range of 1 to 1000 nanometers.

As used herein, the term smooth surface 117 is characterized assatisfying the following condition 1>cos θa>−0.65, where ea is theintrinsic advancing contact angle 140 of a liquid droplet 145 located onthe micro-nucleation site. As illustrated for the embodiment shown inFIG. 1, the smooth surface 117 is free of nanostructures 120, that is,there are no fabricated nanostructures 120 on the smooth surface 117.

The surface energies of the smooth surface 117 and the group 122 of tops125, are inversely proportional to the intrinsic advancing contact angle140, ea, of a droplet on the surface of interest. That is, the lower theangle 140 of a liquid droplet on a surface, the higher the surfaceenergy of that surface, and, the higher the apparent contact angle ofthe droplet on the surface, the lower the surface energy of the surface.

As used herein, the group 122 of tops 125 refers to the minimum numberof top 125 needed to support a liquid droplet thereon in a Cassie state.A person of ordinary skill in the relevant arts would understand thatCassie state refers to wetting state of the droplet where the dropletrests on the tops 125 (e.g., group 122 of tops 125) of thenanostructures 120 in the vicinity of the droplet. For instance, in somecases, less than 10 percent of the nanostructure 120 nearest the tops125 of the group supporting the droplet is in contact with the dropletwhen the droplet is in a Cassie state. When in a Cassie state, most ofthe droplet is not in contact with the nanostructures 120, so that thedroplet's adhesion to the nanostructures 120 is reduced.

A person of ordinary skill in the relevant arts would understand how theminimum number of tops 125 in the group 122 would vary in accordancewith the physical properties of the nanostructures 120, the droplet'scomposition and the dimension and spatial separation of nanostructures.In some embodiments, for example, the group 122 includes at least about5 tops 125, and in some cases more preferably, at least about 10 tops125 of nanostructures 120. The tops 125 in a group 122 are all in thesame vicinity as each other, e.g., such that each nanostructure in agroup 122 is at least adjacent to two other nanostructures in the group122.

As illustrated in FIG. 1, in some embodiments, the micro-nucleationsites 115 and the nanostructures 120 are located on a planar surface 150of the base layer 110. In some cases, the smooth surface 117 can be aplanar surface that is parallel with the planar surface 150 of the baselayer. In other case, the smooth surface 117 can be a planar surfacethat is non-parallel (i.e., sloped) with respect to the planar surface150 of the base layer 110. In still other cases, the smooth surface 117can be non-planar and the surface 150 of the base layer 110 can benon-planar.

As also illustrated in FIG. 1, in some embodiments of the apparatus 100,the tops 125 of the nanostructures 120 are substantially co-planar(e.g., within 10 percent of the height) with each other and with thesmooth surface 117 of the micro-nucleation sites 115. However, in otherembodiment, the top 125 are not all co-planar with each other, e.g.,there can be local upward or downward sloping gradients of tops 125,provided by nanostructures 115 having different heights, in the vicinityof the micro-nucleation sites 115.

As illustrated in FIG. 2, in some embodiments of the apparatus 100, thenanostructures 120 surround each of the micro-nucleation sites 115 onthe base layer 110. For instance, as illustrated, there can be atwo-dimensional array of nanostructures 120 surrounding themicro-nucleation sites 115. As illustrated, in some cases, thenanostructures 120 of the two-dimensional array can be uniformlydimensioned and spaced apart from each other. In still otherembodiments, however, there can be discrete groups 122 of nanostructures120 around the micro-nucleation sites 115. In still other embodiments,there can be progressively (e.g., monotonically) increasing ordecreasing distances separating the nanostructures 120 along one or moredirections parallel to the base layer 110.

As illustrated in FIG. 3A, in some embodiments of the apparatus 100, thesmooth surface 117 of each of the micro-nucleation sites 115 aresubstantial coplanar with bottoms 135 of the nanostructures 120 thatcontact the base layer 110. In some such embodiments, for instance,portions of the base layer 110 can serve as the micro-nucleation sites115. In other cases, micro-nucleation sites 115 can be provided by athin material layer 310 on the base layer 110, where the thickness 315of the material layer is less than 10 percent of a height of thenanostructures 120 above the surface 150 of the base layer 110.

Referring again to FIGS. 1-3A, in some embodiments, to promote dropletnucleation and nascent growth at micro-nucleation sites 115, the smoothsurface 117 of the micro-nucleation sites 115 is a hydrophilic surface,and, to promote mature droplet movement to the tops 125 of thenanostructures 115, the group 122 of the tops 125 of the nanostructures120 is a superhydrophobic surface (synonymous with the term non-wettingsurface as used herein).

As used herein, a surface is considered to be a hydrophilic surface(synonymous with the term wetting surface as used herein) when a liquiddroplet 145 laying on the surface has a contact angle 140 of less orequal to about 90 degrees. As used herein, a surface is considered to bea superhydrophobic surface when a liquid droplet of the liquid laying onthe surface has a contact angle 140 of less than or equal to about 90degrees.

As illustrated in FIG. 2, in some embodiments of the apparatus 100, atleast some of the micro-nucleation sites 115 are separated from eachother by uniform distances 210. FIG. 2 depicts the sites 115 arranged ina square grid pattern. In other embodiments, for example, to optimizethe packing density of sites 115 on the base layer 110, the sites 115arranged in other patterns such as equilateral triangular, pentagonal,hexagonal or other patterns.

In some embodiments, the separation distance 210 between adjacent onesof the micro-nucleation sites 115 is less than a droplet diameter wheredroplet growth becomes heat conduction limiting. It is recognized thatas droplets form and grow on a surface covered with nanostructures, asthe droplet gets to a certain critical size, heat conduction through thebulk of the droplet begins to limit the heat transfer rate.

Consider, for instance, the case where for droplets 145 having a radius155 (FIG. 1) of about 5 microns or greater, further droplet growthbecome heat conduction limited. Such may be the case for a water dropletunder certain environmental conditions, for example. To promote dropletjumping in some such embodiments, the separation distance 210 betweenadjacent ones of the micro-nucleation sites 115 are designed to be equalto or less than about 10 microns.

Having a certain minimum separation distance 210 between themicro-nucleation sites 115 can promote droplet jumping, therebyenhancing heat transfer. For instance, there can be a characteristicdroplet radius, below which viscous effects dominate to suppress dropletjumping. In such instances, if droplets growing on adjacent sites 115are permitted to coalesce prematurely, if the sites 115 are too close toeach other, then the jumping of the merged droplet may be deterred,e.g., because a high adhesion energy has to be overcome. On the otherhand, keeping the sites 115 a certain minimum separation distance 210can facilitate droplet growth on the individual sites 115 to a matureenough size, such that when the droplets grown on adjacent sitescoalesce, the merged drop will spontaneously jump.

Consider, for instance, the case where it is undesirable to allowdroplets to coalesce when the droplet radius is 0.5 microns or less.Such may be the case for a water droplet under certain environmentalconditions, for example. Therefore in some such embodiments theseparation distance between adjacent ones of the micro-nucleation sites115 are preferably equal to or greater than about 1 micron.

Combining the above two considerations can help determine an optimalrange for the separation distance 210 between sites 115 to promoteefficient heat transfer. Continuing with the same example, in someembodiments the apparatus 100 the separation distance 210 betweenadjacent ones of the micro-nucleation sites 115 is in a range of about 1to 10 microns.

It is desirable for each micro-nucleation site 115 to be size so as toprovide as large an area as possible for droplet nucleation and growth,but not so large a surface area that the droplet will adhere to thesurface as it grows beyond the area of the micro-nucleation site 115.For instance, in some embodiments, an area occupied by the smoothsurface of the micro-nucleation sites is in a range of 1 to 100microns². For instance in some embodiments when a micro-nucleation site115 is circular in shape, the micro-nucleation site 115 has a radius 215in a range of 1 to 10 microns, and can have an area range of 1 to 78microns².

FIG. 3B presents a cross-sectional view of yet another embodiment of theapparatus 100 analogous to the view depicted in FIGS. 1 and 3A. Theapparatus 100 depicted in FIG. 3B illustrates various features, which incombination with the micro-nucleation sites 115, are expected to beparticularly advantageous for promoting condensation heat transfer oflow surface tension liquids, such as organic liquids (e.g.,unsubstituted or unsubstituted, alkanes, alkenes, alcohols and ketones)and refrigerants (e.g., hydrocarbons, fluorocarbons or halocarbons).Although the disclosed features are shown in combination, any of thesefeatures could used alone or in lesser combinations for any of theembodiments of the apparatus 100 discussed herein.

It is believed that when a liquid droplet 145 jumps from amicro-nucleation site 115 it is preferred that a remnant droplet portion320 of the liquid remains on the site 115. For instance, the remnantdroplet portion 320 can have a radius of curve in the micron scale, ascompared with a newly formed (nascent) droplet, which may have a radiusof curvature the nanometer scale. The remnant droplet portion 320 helpbypass the early stages of nascent droplet growth associated with thelarge curvature of small droplets that present a high thermal resistanceto droplet growth. Bypassing the early stage of droplet growth istherefore expected to further improve the heat transfer efficiency ofthe apparatus 100. In some embodiments, to promote such droplet growthoccurring predominantly from remnant droplet portion 320 located at themicro-nucleation site 115, is it desirable to deter droplet nucleationin the vicinity of the nanostructures 120, e.g., on the nanostructures120 and on the base layer 110 in-between the nanostructures 120.

It is believed that one way to deter droplet nucleation in the vicinityof the nanostructures 120 is to reduce the local supersaturation in thevicinity of the nanostructures 120. As used herein supersaturation isdefined as the ratio of the vapor pressure to the saturation pressure atthe condensing surface temperature. The local supersaturation in thevicinity of the nanostructures 120 can be reduced by locating thenanostructures 120 adjacent to a lower thermal conductively portion ofthe surface 150 of the base layer 110 as compared to the portion of thebase layer that the micro-nucleation sites 115 are adjacent to. It isbelieved that in such embodiments, the temperature of the surface 150having the low thermal conductively layer 327 will be higher than thetemperature of the surface 117 of the micro-nucleation site 115 andtherefore droplet formation and growth will preferably occur at themicro-nucleation site 115.

For instance, as illustrated in FIG. 3B, in some cases, it isadvantageous for the base layer 110 to be composed of a high thermalconductivity material such as copper or aluminum of similar metals andfor the micro-nucleation site 115 to be adjacent of such a portion 325of the base layer 110. In some cases, it is also advantageous for thebase layer 110 to further include a low thermal conductively portion(e.g., layer 327) located adjacent to the nanostructures 120 thereon.Suitable materials for the low thermal conductively layer 327 includethermally insulating organic polymers or inorganic oxides, such assilicon oxide. Such that the micro-nucleation site 115 is in directcontact with the high thermal conductivity base layer and thenanostructures 120 are insulated from the high thermal conductivity baselayer by the insulating layer 327.

As illustrated in the expanded view shown in FIG. 3B another way todeter droplet nucleation in the vicinity of the nanostructures 120, isto configure the tops 125 of the nanostructures 120 to include areentrant angled ledge 330. As used herein, the term reentrant angledledge 330 refers to a layer on a post portion 335 of the nanostructure120 that forms an interior angle 340 with the post portion 335 ofgreater than 180 degrees. A person of ordinary skill in the relevantarts would be familiar with how to fabricate such nanostructures, e.g.,such a disclosed in Ahuja et al. “Nanonails: A Simple GeometricalApproach to Electrically Tunable Superlyophobic Surfaces” (Langmuir2008, 24, 9-14) which is incorporated by reference herein in itsentirety. It is believed that reentrant angled ledge 330 of suchnanostructures 120 reduces a droplet's ability to de-pin and jump fromthe nanostructures 120 which in turn would deter new droplet nucleationon the nanostructure 120.

As illustrated in FIG. 3B, still another way to deter droplet nucleationin the vicinity of the nanostructures 120 is to infuse a low surfaceenergy liquid 350 in the spaces between the nanostructures 120. Examplesof suitable low surface energy liquid are described in Wong et al.,“Bioinspired self-repairing slippery surfaces with pressure-stableomniphobicity” (Nature 2001, 477, 443) which is incorporated byreference herein in its entirety. It is believed that droplets on suchliquid infused nanostructures 120 would have reduce ability to de-pinand jump from the nanostructures 120 which in turn would deters newdroplet nucleation on the nanostructure 120.

FIG. 4 presents a detailed cross-sectional view of a portion of anapparatus 100, such as the apparatus 100 presented in FIG. 1, depictingexample nanostructures 120 of the apparatus 100. As illustrated, thenanostructure 120 can be pillar-shaped, and, the pillars are spacedapart from each other. In other embodiments, the nanostructures 120 canbe ridged-shaped and the ridges are spaced apart from each other.

The presence of nanostructures 120 beneficially provide a low-energysurface (e.g., non-wetting or super hydrophobic surface) in contrast tothe higher surface energy of the smooth surface 117 of themicro-nucleation sites 115. This is advantageous over conventionalcondensing surfaces because droplet adhesion to the condensation surfacecan be reduced with the appropriate nanostructure configuration. Dropletadhesion to the condensation surface can be reduced with the appropriatenanostructure configuration. In particular, to reduce adhesion, it isdesirable for nanostructures to be configured to facilitate the droplettaking on a Cassie state. There are several structural attributes thatthe nanostructures 120 can have to facilitate a droplet attaining aCassie state.

For instance, in some preferred embodiments, it is desirable for thenanostructures 120 to provide the condensation surface with a certainsurface roughness to deter a droplet from taking on an undesirableWenzel state. A Wenzel state refers to a wetting state where the dropletsubstantially contacts the entire surfaces of the nanostructures 120 inthe vicinity of the droplet. For example, in a Wenzel state,substantially the entire height of the droplet may contact the sides130, 132 and tops 125 of the nanostructures 120 as well as the baselayer 110. In various embodiments, it is often undesirable that adroplet take Wenzel states, because the large contact area of thedroplet in such a state can provide a large adhesion that pins thedroplet in-between the nanostructures 120. Wenzel state formationtherefore impedes the droplet from moving away from its nucleation siteto the apexes 135 of the microstructures 115, which in turn may reducethe efficiency of condensation heat transfer.

To help avoid growing droplets taking such a Wenzel state, it isdesirable for the nanostructures 120 to have the following condition tosatisfy the following condition when a liquid droplet 145 rests on thesurface: −1/r*cos θa<1. Herein, the surface roughness factor, r, isdefined as the total surface area, including the areas of the sides andtops and support surfaces 150 in between the nanostructures 120, dividedby a projected surface area of the surfaces 150, e.g., the area supportsurfaces 150 with no nanostructures 120 thereon. Herein a is anintrinsic advancing contact angle 140 of the liquid droplet 145. Theintrinsic advancing contact angle, ea, refers to the contact angle thatthe liquid droplet would have on a smooth surface, e.g., the supportsurfaces 150 with no nanostructures 120 thereon. In some embodiments,the smooth surface 117 of the nucleation sites 115 follow the condition1>cos θa>−0.65, and the group 122 of tops 125 of the nanostructuresfollow the condition −1/r*cos θa<1.

Although the smooth surface 117 of the nucleation sites 115 are designedto promote droplet nucleation and nascent growth thereon, dropletnucleation and growth may still occur, e.g., concurrently, between thenanostructures 120. In some cases, it may be desirable for thenanostructures 120 to be spaced apart by a minimal separation distance410 (e.g., the distance from the side 130 of one nanostructure 120 tothe side 132 of an adjacent nanostructure 120) to promote droplets toform and grow in-between the nanostructures 120.

In some such cases, the distance 410 is preferably greater than acritical condensation radius 155, r_(c), for a nucleating liquiddroplet. The critical condensation radius can be estimated by theformula:

r _(c)=2γυ/(kTlnS),

Here, γ is the ratio of liquid to vapor surface tension, υ is amolecular volume of the liquid phase, k is the Boltzmann constant, andS, the saturation, is defined as the ratio of the vapor pressure pv tothe saturation pressure at the condensing surface temperature T. Forexample, in some embodiments of the device 100, for a water droplet, thedistance 410 separating adjacent nanostructures is equal to of greaterthan about 10 nanometers. For example, in some embodiments of theapparatus 100, the distance 410 is in a range of about 1 to 100nanometers, and in some cases in a range of about 10 to 20 nanometers.

In some such cases, the distance 410 between adjacent ones of thenanostructures 120 preferably has a value that promotes a droplet toattain the Cassie state before the droplet radius 155, R, grows to sizethat is heat conduction limiting. For example, for water droplet thisvalue of the radius 155 is about 5 microns or larger. The Cassie state,is promoted by spacing the nanostructures apart by preferred distance320 and by having a height 420 that facilitates the droplet 145 have areceding contact angle 140, θr, of at least about 90 degrees.

For instance, in some preferred embodiments, the nanostructures follow arelationship:

cos θ_(r)<−(1+h/R)/(1+2h/w),

Here θ_(r) is a receding contact angle 140 of at least about 90 degreesfor maximally desired size of droplet located on tops of thenanostructures, h is the uniform heights 420 of the nanostructures 120,R is a radius 155 of the liquid droplet and w is a uniform separationdistance 410 between adjacent ones of the nanostructures 120.

As used herein, the term receding contact angle 140 is defined as theminimum stable angle that the droplet 145 achieves while on thenanostructures 120. A person of ordinary skill in the relevant artswould be familiar with methods to measure the receding contact angle 140of a droplet (see e.g., “Condensation on. Superhydrophobic Surfaces: TheRole of Local Energy Barriers and Structure Length Scale” and SupportingInformation, by Enright et al., Langmuir pub. Aug. 29, 2012(“Enright-1”), incorporated by reference herein in its entirety).

The receding contact angle 140 for a droplet to spontaneously achieve aCassie state can be reduced by minimizing the ratio h/R and/ormaximizing the ratio h/w. For example, in some embodiments, a ratio of aheight 420 of the nanostructures 120 to a radius 155, R, of a maximallysized liquid droplet on the surface (e.g., the h/R ratio) is equal to orless than about 0.1:1. For example, in some embodiments, a ratio of aseparation distance 410, w, to the height 420 of the nanostructures isin a range from about 0.5:1 to 30:1, and more preferably about 0.5:1 to3:1.

For instance, consider a liquid whose critical size, where heatconduction through the bulk of the droplet begins to limit the heattransfer rate, and, that critical size corresponds to a droplet radius155 of 5 microns or greater. Assuming a desired receding contact angle140, θ_(r), equal to 120 degrees, to make the ratio of h, the uniformheight 420 of the nanostructures 305 to R, a radius 410 of the liquiddroplet less than or equal to 0.1 (i.e., h/R≦0.1) requires h≦0.5 μm. Fora h/R ratio equal to 0.1 and the height 420, h, equal to 0.5 μm, theseparation distance 320 between microstructures, w, is then equal to 833nanometers and the h/w ratio equals 0.6. Continuing with the sameexample, where the h/R ratio equals 0.1 and h equals 0.5 μm, for areceding contact angle 140, θ_(r), equal to 110 degrees, w, is thenequal to 451 nanometers and the h/w ratio equals 1.1, or, for a recedingcontact angle 140, θ_(r), equal to 100 degrees, w, is then equal to 187nanometers, and the h/w ratio equals 2.7, or, for a receding contactangle 140, θ_(r), equal to 90 degrees, w, is then equal to 16nanometers, and the h/w ratio equals 31.3.

In some embodiments of the apparatus 100, to reduce the adhesion of ade-wetted droplet (e.g., a droplet in a Cassie state) it is desirable toreduce the fraction of space occupied by the nanostructures 120 relativeto the open space in-between adjacent ones of the nanostructures. Forinstance, in some embodiments, the solid fraction occupied by thenanostructures 120 is equal to or less than 0.1. As used herein the termsolid fraction herein is equal to d/(d+w), where d is the width 430 ofthe nanostructure and w is the separation distance 410 between adjacentones of the nanostructures 120.

As a non-limiting example, in cases where the separation distance 410 isequal to 833 nanometers, then the width 430 is preferably equal or lessthan 93 nanometers. Or, when the separation distance 410 is equal to 451nanometers, then the width 430 is preferably equal or less than 50nanometers. Or, when the separation distance 410 is equal to 451nanometers, then the width 430 is preferably equal or less than 50nanometers. Or, when the separation distance 410 is equal to 187nanometers, then the width 430 is preferably equal or less than 21nanometers. Or, when the separation distance 410 is equal to nanometers,then the width 430 is preferably equal or less than 1.8 nanometers.

Another embodiment is a method that comprises manufacturing an apparatus(e.g., a heat transfer apparatus).

With continuing reference to FIGS. 1-4 throughout, FIG. 5 presents aflow diagram of an example method of manufacturing a heat transferapparatus, such as any of the apparatuses 100 described in the contextof FIGS. 1-4. As illustrated in FIG. 5, the method includes a step 505of manufacturing an apparatus 100, which in some cases can be or includea condenser 105. Manufacturing the apparatus (step 505) includes a step510 of providing a base layer 110 and step 515 of formingmicro-nucleation sites 115 on the base layer 110. Each of themicro-nucleation sites 115 has a smooth surface 117. The method alsoincludes a step 520 of forming nanostructures 120 on the base layer 110and around the micro-nucleation sites 115, wherein a group 122 of tops125 of the nanostructures 120 have a lower surface energy than a surfaceenergy of the smooth surface 117.

To further illustrate aspects of the method described in FIG. 5, FIGS.6A-6C present cross-sectional views of an example apparatus 100, similarto the apparatus 100 shown in FIG. 1, at intermediate stages offabrication for one embodiment of the method. FIGS. 7A-7D presentscross-sectional views of an example apparatus 100, similar to theapparatus 100 shown in FIG. 3A, at intermediate stages of fabricationfor another embodiment of the method.

Referring to FIGS. 5, and 6A or 7A, in some embodiments of the method,providing the base layer 110 in step 510 can include providing a singlematerial layer 610, e.g., a layer of copper, aluminum, or semiconductormaterial, upon which the micro-nucleation sites 115 are directly formedfrom in step 515. In some cases the use of a highly heat conductivematerial layer 610 such copper, aluminum or similar metals, ispreferred. In other cases, the providing the base layer 110 in step 510can include a step 525 of forming a second material layer 620 on thefirst material layer 610. In such cases, for example, themicro-nucleation sites 115 and/or nanostructures 120 can be formed fromthe second material layer 620. For instance, a second material layer 620of copper or aluminum could be deposited on a first material layer 610of steel, via electrolytic, electroless or other deposition processesfamiliar to a person of ordinary skill in the relevant arts. Or amaterial layer 620 of silicon oxide, silicon or other semiconductormaterial layer could be deposited or grown on silicon or othersemiconductor layer 610. Or a low thermal conductivity material layer620 could be selectively formed over a high thermal conductivitymaterial layer 610. For instance, the low thermal conductivity layer 327can be deposited so as to surround portions 325 of the high thermalconductivity base layer 110, such as depicted in FIG. 3B.

In some embodiments of the method, forming the one or moremicro-nucleation sites 115 (step 515) includes a step 530 of forming amask layer on the base layer 110 and step 532 of patterning the masklayer such that mask portions 625 (FIG. 6A 7A) remain on the base layer110 in locations corresponding to the micro-nucleation sites 115. Aperson of ordinary skill in the relevant arts would be familiar withprocedures for depositing a mask layer, such as a photoresist mask layerand how to pattern the mask layer, e.g., using standardphotolithographic processes, to form the mask portions 625.

In some embodiments of the method, as illustrated in FIG. 6B, formingthe nanostructures 120 (step 520) includes a step 535 of modifying thebase layer 110 (e.g., one of layer 610 or layer 620 if present) notcovered by the mask portions 625 that are located on the base layer 110and that correspond to the locations of the micro-nucleation sites 115.

In some embodiments of the method, forming the one or moremicro-nucleation sites 115 (step 515) can also include a step 540 ofremoving the mask portions 625 to uncover the micro-nucleation sites115, e.g., such that tops 125 of the nanostructures 120 aresubstantially coplanar with the smooth surface 117 of themicro-nucleation sites 115, such as illustrated in FIG. 1. A person ofordinary skill in the relevant arts would be familiar with to remove amask portion such as a mask portion composed of photoresist material.

As illustrated in FIG. 6C, in some embodiments of the method, formingthe nanostructures 120 (step 520) include a step 545 of functionalizingoutside surfaces of the nanostructures with a low surface energymaterial 630 as further illustrated in the expanded view presented inthe figure. In some cases, it is preferable for step 545 to be performedbefore removing the mask portions 625 so that the smooth surface 117 ofthe sites 115 is not similarly functionalized.

In some embodiments of the method, as illustrated in FIG. 7B, formingthe nanostructures 120 (step 520) includes, after the steps 525, 530 offorming a mask layer and patterning the mask layer to form the markportions 625, a step 550 of forming a material layer (e.g., layer 620)on the base layer 110 (e.g., layer 610) and the mask portions 625.Forming the nanostructures 120 (step 520) can then include a step 555 ofmodifying the material layer 620 on the base layer 110 and mask portions625 to form the nanostructures 120, such as illustrated in FIG. 7C.

As illustrated in FIG. 7D, forming the nanostructures 120 (step 520) inembodiments can also include the step 545 of functionalizing outsidesurfaces of the nanostructures 115 with the low surface energy material630, as illustrated in the expanded view. Once again in some cases, itis preferable for step 545 to be performed before removing the maskportions 625 so that the smooth surface 117 of the sites 115 is notsimilarly functionalized.

Forming the one or more micro-nucleation sites 115 (step 515) can alsoinclude the step 540 of removing the mask portions 625 to uncover themicro-nucleation sites 115, e.g., such that bottoms 135 of thenanostructures 120 are substantially coplanar with the smooth surface117 of the micro-nucleation sites 115, such as illustrated in FIG. 3A.

In some embodiments, modifying the base layer 110 (including layer 610in some cases) or material layer 620 in accordance with step 535 or 555can include exposing at least one these layers 110, 610, 620 to anoxidation process. For instance, a copper base layer 110 or coppermaterial layer 620 thereon can be exposed to chemical oxidationconditions such as in “Condensation on Supersuperhydrophobic CopperOxide Nanostructures,” by Enright et al. Proceedings of the 3rdMicro/Nanoscale Heat and Mass Transfer International Conference,Atlanta, Ga., Mar. 3-6, 2012 MNHMT2012-75277 (“Enright-2”), incorporatedby reference herein in its entirety, to form the nanostructures 305therefrom. For instance, an aluminum base layer 110 or aluminum materiallayer 620 thereon can be exposed to well-known hydrothermal oxidationprocesses form the nanostructures 305 therefrom.

In some embodiments, modifying the base layer 110 (including layer 610in some cases) or material layer 620 in accordance with step 535 or 555can includes exposing at least one these layers 110, 610, 620 to an etchprocess. For instance, layers 110, 620 composed of a semiconductormaterial, such as silicon, can be subjected to a reactive ion etchingprocess to form the nanostructures 120, such as black siliconnanostructures. Other examples of etching process are presented inEnright-1.

In some embodiments, modifying the base layer 110 (including layer 610in some cases) or material layer 620 in accordance with step 535 or 555can include mechanically modifying portions of at least one of theselayers 110, 610, 620. For instance, a layer of copper, aluminum ofsemiconductor material can be mechanically indented, machined, stamped,embossed or otherwise mechanically modified to form the nanostructures120.

As used herein, the term low surface energy material 630, refers to amaterial having a surface energy of about 22 dynes/cm (about 22×10⁻⁵N/cm) or less as disclosed in U.S. Pat. No. 7,695,550 to Krupenkin etal. (“Krupenkin”), incorporated by reference herein in its entirety. Aperson of ordinary skill in the relevant arts in the art would befamiliar with the methods to measure the surface energy of materials.

Non-limiting examples of functionalizing nanostructures in accordancewith step 545 includes coating the nanostructures 120 withchlorosilanes, fluorosilanes or fluorinated polymers, such as disclosedin Krupenkin, Enright-1 or Enright-2.

FIG. 8 illustrates another embodiment of the disclosure, a system 800.In some embodiments, the system 800 can be communication system such asa telecommunication system or a system component (e.g., an electroniccabinet) of a communication system. The system 800 comprises heatgenerating equipment 810, such electrical equipment, e.g., circuitboards having heat generating components thereon. The system 800 alsocomprises a heat transfer apparatus 820. The heat transfer apparatus 820can be configured to remove heat generated by the equipment 810 of thesystem 800.

The heat transfer apparatus 820 can be or include any apparatusesdescribed herein. In some cases, for instance, referring to FIGS. 1-4,the apparatus 820 includes a base layer 110 having one or moremicro-nucleation sites 115 thereon, wherein each of the micro-nucleationsites 115 has a smooth surface 117. The apparatus also includesnanostructures 120 located on the base layer 110 and around themicro-nucleation site 115. Tops 125 of the nanostructures 120 (e.g., agroup 122 of top 125) have a lower surface energy than a surface energyof the smooth surface 120.

With continuing reference to FIGS. 1-4, in some embodiments of thesystem 800, the micro-nucleation sites 115 are located on the surface ofa condenser 105 of the apparatus 100. In some embodiments, the condenser105 is part of a heat pipe (e.g., serving as the base layer 110), whilein other embodiments, the condenser 105 is part of a vapor chamber(e.g., serving as the base layer 110).

Although the present disclosure has been described in detail, a personof ordinary skill in the relevant arts should understand that they canmake various changes, substitutions and alterations herein withoutdeparting from the scope of the invention.

1. An apparatus, comprising: a base layer having a distribution ofseparated micro-nucleation sites thereon; and a distribution ofnanostructures located on the base layer, each of the micro-nucleationsites being adjacent to some of the nanostructures; and wherein each ofthe micro-nucleation sites has a hydrophilic surface and thedistribution of nanostructures form a superhydrophobic surface.
 2. Theapparatus of claim 1, wherein the micro-nucleation sites and thenanostructures are located on a planar surface of the base layer.
 3. Theapparatus of claim 1, wherein tops of the nanostructures aresubstantially coplanar with the hydrophilic surfaces of themicro-nucleation sites.
 4. The apparatus of claim 1, wherein some of thenanostructures surround each of the micro-nucleation sites.
 5. Theapparatus of claim 1, wherein the hydrophilic surfaces of each of themicro-nucleation sites are substantially coplanar with bottoms of thenanostructures that contact the base layer.
 6. The apparatus of claim 1,wherein an area occupied by the hydrophilic surfaces of each of themicro-nucleation sites is in a range of 1 to 100 microns².
 7. Theapparatus of claim 1, wherein the hydrophilic surface of each of themicro-nucleation sites has a smooth surface.
 8. The apparatus of claim1, wherein a separation distance between adjacent ones of themicro-nucleation sites is equal to or less than about 10 microns.
 9. Theapparatus of claim 1, wherein the nanostructures are located on a regionof the base layer having a lower thermal conductivity than a region ofthe base layer having the micro-nucleation sites thereon.
 10. Theapparatus of claim 1, wherein tops of the nanostructures include areentrant angled ledge.
 11. The apparatus of claim 1, wherein an area ofthe base layer having the nanostructures located thereon has a surfaceroughness where the following condition applies when a liquid dropletrests on the surface: −1/r*cos θa<1, wherein r is the surface roughnessof the surfaces having the distribution of nanostructures locatedthereon and θa is an intrinsic advancing contact angle of the liquiddroplet.
 12. The apparatus of claim 1, wherein a distance betweenadjacent ones of the nanostructures is greater than a criticalcondensation radius for a nucleating liquid droplet on the surface. 13.A system, comprising: heat generating equipment; and a heat transferapparatus configured to remove heat generated by the heat generatingequipment, wherein the apparatus includes: a base layer having adistribution of separated micro-nucleation sites thereon; and adistribution of nanostructures located on the base layer, each of themicro-nucleation sites being adjacent to some of the nanostructures; andwherein each of the micro-nucleation sites has a hydrophilic surface andthe distribution of nanostructures form a superhydrophobic surface. 14.The system of claim 13, wherein the micro-nucleation sites are locatedon the surface of a condenser of the apparatus.
 15. The system of claim13, wherein the condenser is part of a heat pipe or a vapor chamber. 16.A method, comprising: manufacturing an apparatus, including: providing abase layer; forming a distribution of separated micro-nucleation siteson the base layer, wherein each of the micro-nucleation sites has ahydrophilic surface; and forming a distribution nanostructures on thebase layer, wherein each of the micro-nucleation sites being adjacent tosome of the nanostructures.
 17. The method of claim 16, wherein formingthe micro-nucleation sites includes: forming a mask layer over the baselayer; and patterning the mask layer such that mask portions remain onthe base layer in locations corresponding to the micro-nucleation sites.18. The method of claim 16, wherein forming the nanostructures on thebase layer includes: modifying portions of the base layer not covered bymask portions located on the base layer that correspond to locations ofthe micro-nucleation sites.
 19. The method of claim 18, wherein formingthe micro-nucleation sites includes: removing the mask portions touncover the micro-nucleation sites such that tops of the nanostructuresare substantially coplanar with the hydrophillic surfaces of themicro-nucleation sites.
 20. The method of claim 16, wherein forming thenanostructures on the base layer includes: forming a mask layer over thebase layer; patterning the mask layer such that mask portions remain onthe base layer corresponding to locations of the micro-nucleation sites;forming a material layer on the base layer and the mask portions; andmodifying the material layer on the base layer and the mask portions toform the nano structures.